Graded cellular bases for Temperley-Lieb algebras of type A and B

We show that the Temperley-Lieb algebra of type $A$ and the blob algebra (also known as the Temperley-Lieb algebra of type $B$) at roots of unity are $\mathbb Z$-graded algebras.We moreover show that they are graded cellular algebras, thus making their cell modules, or standard modules, graded modules for the algebras.Comment: 36 pages. Final version, to appear in Journal of Algebraic Combinatoric

The effect of background knowledge on young children's comprehension of explicit and implicit information

Bibliography: leaves 15-16Supported in part by the National Institute of Educatio

Unions and the Sword of Justice: Unions and Pay Systems, Pay Inequality, Pay Discrimination and Low Pay

Dispersion in pay is lower among union members than among non-unionists. This reflects two factors. First, union members and jobs are more homogeneous than their non-union counterparts. Second, union wage policies within and across firms lower pay dispersion. Unions' minimum wage targets also truncate the lower tail of the union distribution. There are two major consequences of these egalitarian union wage policies. First, the return to human capital is lower in firms which recognise unions than in the unorganised sector. Second, unions compress the wage structure by gender, race and occupation.Unions, pay distribution, discrimination

A Sin of Omission: Database Transactions

Database courses are under increasing pressure to include new topics which inevitably leads to a decision about which topics are essential to the course and which can be omitted to make room for others. Recent surveys have indicated that many instructors are reducing or eliminating coverage of “transaction management” from their introductory database courses. As both an academic and a practitioner, I believe that this is a mistake. This paper discusses why the semantics of transaction management should be an integral topic in any introductory database management system course